Level E
Algebra
Tidying up terms
www.mathsrevision.com
Number Machine
Working with Expressions
Solving Simple Equations
Solving Harder Equations
Understanding Inequalities
Solving Simple Inequalities
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Starter Questions
2
Q1. Calculate 66 % of £270
3
www.mathsrevision.com
Q2. Convert 60% to fraction and simplify.
4
Q3. Convert to a percentage.
5
Q4. What is the time difference 09:28 and 10:50
Q5. The answer to the question is 90. What is the
question.
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Aim of the Lesson
Tidying Terms
www.mathsrevision.com
a+2b+3a+b
1. Tidying up expressions.
2. Show steps when tidying up.
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Tidying Terms
First Row : + + =
www.mathsrevision.com
2c + c + 4c = 7c
2nd Row : + + =
25-Nov-11
2d + 2d +
Created by Mr.Lafferty Maths Dept
3d = 7d
Level E
Tidying Terms
3rd Row : + + =
www.mathsrevision.com
3f + f + 2f = 6f
CANNOT
In Total we have TIDY UP
ANYMORE
7c + 7d + 6f
WE CAN ONLY TIDY UP “LIKE TERMS”
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Tidying Terms
WE CAN ONLY TIDY UP “LIKE TERMS”
www.mathsrevision.com
Tidy up the following:
Q1. 2x+4x+5y-3y+18 6x+5y-3y+18 = 6x+2y+18
Q2. 4a+3b+5a+6-b 9a+3b-b+6 = 9a+2b+6
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Tidying Terms
www.mathsrevision.com
Your turn !
Page 46 Exercise 1
Q1 and Q2
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Starter Questions
Q1. Tidy up the expression 2y+3x+4x+10
www.mathsrevision.com
2
Q2. Calculate of 84
3
Q3. Round to 1 decimal place.
(a) 2.34 (b) 10.25 (c) 3.23
Q4. 12.5 % as a fraction
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Aim of the Lesson
Number Machine
www.mathsrevision.com
1. To build simple expressions.
2. To UNDO simple expressions.
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Number Machine
To build an expression from the number machine
simply follow the rules given:
www.mathsrevision.com
4a
Multiply
a Add 1 4a+1
By 4
7m
Multiply Subtract
7 7m-2
By m 2
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Number Machine
To build an expression from the number machine
simply follow the rules given:
www.mathsrevision.com
Multiply
20
4
By 5
+3 23
?
Multiple
3b
3 +9 3b+9
?
by b
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Number Machine
www.mathsrevision.com
Your turn !
Page 93 Exercise 2
Q1
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Number Machine
To UNDO the number machine
simply do the opposite of the rules given:
www.mathsrevision.com
x2 UNDO +8 UNDO
Divide by 18
36
?
2
-8 10
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Number Machine
To UNDO the number machine
simply do the opposite of the rules given:
www.mathsrevision.com
x4 UNDO -9 UNDO
Divide by 5
20
?
4
+9 14
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Number Machine
www.mathsrevision.com
Your turn !
Page 93 Exercise 2
Q3 and Q4
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Starter Questions
1. Simplify a 4a 13d 11a a 3d
www.mathsrevision.com
2. The ratio of apples to pears is 2 : 5.
If there are 28 pieces of fruit in total.
How many apples are there.
3. Find HCF of 8 and 18
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Substitution
Learning Intention Success Criteria
www.mathsrevision.com
1. To explain the process of 1. Understand process of
working out expressions by substitution.
substitution method.
2. Solving expressions
showing working.
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Substitution
1 If a = 3 and b = 9 evaluate
www.mathsrevision.com
a+b
Sub in a=3
= 3+ 9 Sub in b=9
= 12
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Substitution
2 If a = 3 and b = 9 evaluate
www.mathsrevision.com
ab
axb Remember ab means a x b
Sub in a=3
= 3x9 Sub in b=9
25-Nov-11 = 27 Created by Mr.Lafferty Maths Dept
Level E
Substitution
3 If a = 3 and b = 9 evaluate
www.mathsrevision.com
4b
4xb Remember 4b means 4 x
b
= 4x9 Sub in b=9
= 36
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Substitution
If a = 5 and b = 6 evaluate
www.mathsrevision.com
1. a + b =11 4. b - a =1
2. ab =30 5. 4b =24
3. 3a =15 6. 3ab =90
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Substitution
4 If a = 5 and b = 3 evaluate
2a + 4b
www.mathsrevision.com
= 2xa + 4xb Remember 2a means 2 x a
Sub in a=5
= 2x 5 + 4x3 Sub in b=3
= 10 + 12
= 22
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Substitution
5 If a = 5 and b = 3 evaluate
www.mathsrevision.com
a2
= a x a Remember a2 means a x a
Sub in a=5
= 5x 5
= 25
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Substitution
6 If a = 15 and b = 3 evaluate
www.mathsrevision.com
a 15 Remember a means a ÷ b
= b
b 3
Sub in
= 5 a=15
Sub in b = 3
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Substitution
If a = 2 and b = 6 evaluate
www.mathsrevision.com
1) 4a + 3b =26 4) 5b – 3a =24
2) a2 =4 5) 4a2 =16
3) b2 =36 6) b =3
a
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Substitution
www.mathsrevision.com
Your turn !
Page 94 Exercise 3
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Starter Questions
1. Simplify 3 x x 6 x x 3
www.mathsrevision.com
2. The ratio of apples to pears is 3 : 1.
If there are 24 pieces of fruit in total.
How many apples are there.
3. Find LCM of 6 qand 21
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Equations
Level E Solving Equations
Learning Intention Success Criteria
www.mathsrevision.com
1. To solve simple equations 1. Know the process of the
using the „Balancing Method‟.
„Balancing Method‟.
2. Solving simple algebraic
equations.
25-Nov-11 Created by Mr.Lafferty Maths Dept
25-Nov-11 Created by Mr Lafferty Maths Dept
Balancing Method
Kirsty goes to the shops every week to buy some potatoes.
She always buys the same total weight.
One week she buys 2 large bags and 1 small bag.
www.mathsrevision.com
The following week she buys 1 large bag and 3 small bags.
If a small bags weighs 4 kgs. How
much does a large bag weigh? 4
4 4
4
How can we go about
What instrument
solving this using
measures balance
balance ?
25-Nov-11 Created by Mr Lafferty Maths Dept
Balancing Method
Take a small bag away
from each side. 4
www.mathsrevision.com
4 4 4
Take a big bag away
from each side.
We can see that a big bag
is equal to
4 + 4 = 8 kg
25-Nov-11 Created by Mr Lafferty Maths Dept
Balancing Method
What symbol should
we use for the scales
?
Let‟s solve it using maths.
4
www.mathsrevision.com
Let P be the weight P P
4
P
4 4
of a big bag.
We know that a small bag = 4
2P + 4 = P + 12 Subtract 4
-4 -4 from each side
2P = P + 8 Subtract P
-P -P from each side
P=8
25-Nov-11 Created by Mr Lafferty Maths Dept
Balancing Method
Group of 5 adults and 3 children go to the local swimming.
Another group of 3 adults and 8 children also go swimming.
www.mathsrevision.com
The total cost for each group is the same.
A child‟s ticket costs £2. 2 a
If a child‟s ticket costs £2. How much 2 a a
for an adult ticket ? 2 2 2 2
a
a a 2 2 2 2
Let a be the price a a 2
of an adult ticket.
We know that a child price = £2
25-Nov-11 Created by Mr Lafferty Maths Dept
Balancing Method
Subtract 6
Subtract 3a
For balance we have each side
from
2 a
www.mathsrevision.com
2 a a
5a + 6 = 3a + 16 a 2
-6 -6 a a 2 2 2 2
a a 2 2 1
2 2
5a = 3a + 10
-3a -3a
Divide each
2a = 10 side by 2
a= 5
Adult ticket price is £5
25-Nov-11 Created by Mr Lafferty Maths Dept
Balancing Method
www.mathsrevision.com
It would be far too time consuming to draw out
the balancing scales each time.
We will now learn how to use the rules for
solving equations.
Level E
Equations
Level E Solving Equations
The method we use to solve equations is
www.mathsrevision.com
The Balancing Method
Write down the opposite of the following :
+ -
opposite is - opposite is +
x opposite is ÷ ÷ opposite is x
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Equations
Level E Solving Equations
The Balancing Method
www.mathsrevision.com
Subtract
Add 5 to
8 from
each side
Examples each side
x 5 11 x8 8
x 11 5 x 88
x 16 x0
Check to see if correct ! Check to see if correct !
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Equations
Level E Solving Equations
The Balancing Method
www.mathsrevision.com
Divide
Divide each side
each side by 8
Examples by 3
3 y 18 8m 72
18 72
y m
3 8
y6 m9
Check to see if correct ! Check to see if correct !
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Equations
Level E Solving Equations
www.mathsrevision.com
Now try Exercise 4
Ch8 (page 96)
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Starter Questions
1. Simplify 5 y 6 x 7 x 3 x 3 xy
www.mathsrevision.com
2. The ratio of apples to pears is 4 : 5.
If there are 72 pieces of fruit in total.
How many apples are there.
3. Find HCF of 15 and 21
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Equations
Level E Harder Equations
Learning Intention Success Criteria
www.mathsrevision.com
1. To solve harder equations 1. Know the process of
using the rule „Balancing Method‟.
„Balancing Method‟.
repeatedly.
2. Solving harder algebraic
equations by using rule
repeatedly.
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Equations
Level E Harder Equations
The rule we use to solve equations is
www.mathsrevision.com
The Balancing Method
Write down the opposite of the following :
+ -
opposite is - opposite is +
x opposite is ÷ ÷ opposite is x
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Equations
Level E Harder Equations
The Balancing Method
www.mathsrevision.com
Examples Subtract
1 from
2 x 1 11 each side
2 x 11 1 10 Divide
each side
2 x 10 by 2
10
x 5 Check to see if correct !
25-Nov-11
2 Created by Mr.Lafferty Maths Dept
Level E
Equations
Level E Harder Equations
The Balancing Method
www.mathsrevision.com
Examples Add 6 to
each side
4 x 6 30
4 x 30 6 36 Divide
each side
4 x 36 by 4
36
x 9 Check to see if correct !
4
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Equations
Level E Harder Equations
www.mathsrevision.com
Now try Exercise 5
Ch8 (page 97)
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Starter Questions
1. Simplify 7 a 4a 9b 11b ab 3
www.mathsrevision.com
2. The ratio of apples to pears is 6 : 7.
If there are 52 pieces of fruit in total.
How many apples are there.
3. Find LCM of 4 qand 7
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Inequalities
Level E Solving Inequalities
Learning Intention Success Criteria
www.mathsrevision.com
1. To explain the various 1. Know rule the 4 symbols for
symbols for inequalities. inequalities.
2. Solving simple inequalities
equations.
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Inequalities
Level E Solving Inequations
The equations you were solving were called
equations because they contained an “=“ sign.
www.mathsrevision.com
There are 4 other Mathematical symbols
They are called inequalities :
greater than greater than or equal to
less than less than or equal to
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Inequalities
Level E Solving Inequalities
Arrow ALWAYS
points to the
Examples : Write in words what each mean.
smallest number
www.mathsrevision.com
5>3 means 5 is greater than 3
-7 6
(b) -2 and 1 -2 -7
(d) 34 and -35 34 > -35
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Inequalities
Level E Solving Inequalities
Examples : Choosing from -3, -2, -1, 0 , 1, 2, 3
www.mathsrevision.com
(a) y2 3
(c) y ≤ -2 -3, -2
(d) y>3 No solution
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Inequalities
Level E Solving Inequalities
www.mathsrevision.com
Now try Exercise 6
Ch8 (page 99)
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Starter Questions
1. Simplify 10 y 2 2 y 8 y 2 3 y 3 y
www.mathsrevision.com
2. The ratio of apples to pears is 5 :14.
If there are 57 pieces of fruit in total.
How many pears are there.
3. Find LCM of 6 and 10
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Inequalities
Level E Inequalities
Learning Intention Success Criteria
www.mathsrevision.com
1. To solve simple inequalities 1. Know rule
using the same rules as for „change side change sign‟.
equations
„change side change sign‟.
2. Solving simple inequalities
equations.
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Inequalities
Level E Inequalities
The Good News
www.mathsrevision.com
Same rule as solving equations
The Balancing Method
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Inequalities
Level E Solving Inequalities
The Balancing Method
www.mathsrevision.com
Subtract
Add 9 to
10 from
each side
Examples each side
x 9 16 x 10 19
x 16 9 x 19 10
x 25 x9
Check to see if correct ! Check to see if correct !
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Inequalities
Level E Solving Inequalities
The Balancing Method
www.mathsrevision.com
Divide by
Divide by 9 each
7 each side
Examples side
7 y 35 9m 36
35 36
y m
7 9
y5 m4
Check to see if correct ! Check to see if correct !
25-Nov-11 Created by Mr.Lafferty Maths Dept
Level E
Inequalities
Level E Inequalities
www.mathsrevision.com
Now try Exercise 7
Ch8 (page 101)
25-Nov-11 Created by Mr.Lafferty Maths Dept